Poisson bracket in complex canonical coordinates
= Poisson bracket in complex canonical coordinates
For $z_j=q_j+ip_j$ and $\bar z_j=q_j-ip_j$,
$$
\{f,g\}
=-2i\frac{\partial f}{\partial z_j}
\frac{\partial g}{\partial\bar z_j}
+2i\frac{\partial g}{\partial z_j}
\frac{\partial f}{\partial\bar z_j}.
$$
This follows from $\partial_{q_j}=\partial_{z_j}+\partial_{\bar z_j}$ and $\partial_{p_j}=i\partial_{z_j}-i\partial_{\bar z_j}$.